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Three-phase balanced wye-wye system problem

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data
    In a balanced three-phase wye-wye system, the source is an abc-sequence set of voltages and V_an = 120e^(i30°) V rms. The power absorbed by the load is 3435 W and the load impedance is 10 + j2 Ω. Find the two possible line impedance if the power generated by the source is 3774 W. Which line impedance is more likely to occur in an actual power transmission system?

    Z_line = ?
    Z_load = 10+j2 ohm
    P_load = 3435 W
    P_source = 3774 W
    V_s = 120e^(i30°) V rms

    2. Relevant equations

    V_an = I_aA (10 + j2 + Z_line)

    P_s = V_an * I_aA cos θ / sqrt(3)

    3. The attempt at a solution

    I can't seem to figure out a way to solve for any particular variable... I can find that the power of the line, P_line = 339 W, but that's about as far as I can get. The line impedance appears to be solved by:

    Z_line = V_an - I_aA (Z_load) / I_aA
    (derived from first relevant eq.)

    But the current isn't given, and if I derive current I_aA from second relevant equation, then I don't know cos θ. The fact that there is a cos θ, it does make sense that there would be two valid line impedances.

    Any thoughts?
     
  2. jcsd
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